An S-N curve (also known as a Wöhler curve) visualizes the relationship between alternating stress amplitude and the number of cycles to failure for a material under fatigue loading. Both axes typically use logarithmic scales, with stress on the y-axis and cycle count on the x-axis. This plot is fundamental for predicting material fatigue life and identifying key material properties such as ultimate strength, yield strength, and endurance limit.
""" anyplot.ai
sn-curve-basic: S-N Curve (Wöhler Curve)
Library: altair 6.1.0 | Python 3.13.13
Quality: 87/100 | Updated: 2026-05-20
"""
import os
import altair as alt
import numpy as np
import pandas as pd
from PIL import Image
# Theme tokens
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
ELEVATED_BG = "#FFFDF6" if THEME == "light" else "#242420"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"
# Okabe-Ito palette
BRAND = "#009E73" # pos 1 — fatigue test data & Basquin fit
C_UTS = "#C475FD" # pos 2 — Ultimate Tensile Strength
C_YS = "#4467A3" # pos 3 — Yield Strength
C_EL = "#BD8233" # pos 4 — Endurance Limit
# Data — fatigue test results for medium-carbon steel specimens
np.random.seed(42)
A = 800 # Basquin coefficient (MPa)
b = -0.12 # Basquin exponent
stress_levels = np.array([450, 400, 350, 300, 275, 250, 225, 200, 180, 160])
cycles_list, stress_list = [], []
for stress in stress_levels:
theoretical_cycles = (stress / A) ** (1 / b)
n_samples = np.random.randint(3, 6)
scatter = np.exp(np.random.normal(0, 0.3, n_samples))
cycles_list.extend(theoretical_cycles * scatter)
stress_list.extend([stress] * n_samples)
df = pd.DataFrame({"cycles": cycles_list, "stress": stress_list})
# Basquin fit line (smooth curve through full cycle range)
fit_cycles = np.logspace(2, 8, 100)
fit_stress = A * fit_cycles**b
fit_df = pd.DataFrame({"cycles": fit_cycles, "stress": fit_stress})
# Material property reference lines
ref_df = pd.DataFrame({"property": ["UTS: 520 MPa", "YS: 380 MPa", "EL: 150 MPa"], "stress": [520, 380, 150]})
# Infinite-life design zone — subtle band below endurance limit
band_df = pd.DataFrame({"y1": [100], "y2": [150]})
# Region text labels — annotate the three fatigue life zones
region_df = pd.DataFrame(
{
"cycles": [700.0, 150000.0, 800000.0],
"stress": [580.0, 580.0, 125.0],
"label": ["Low-Cycle Fatigue", "High-Cycle Fatigue", "Infinite Life"],
}
)
# Shared log scales
x_scale = alt.Scale(type="log", domain=[100, 1e8])
y_scale = alt.Scale(type="log", domain=[100, 750])
TITLE = "sn-curve-basic · python · altair · anyplot.ai"
# Infinite-life zone fill (band below endurance limit)
band = alt.Chart(band_df).mark_rect(opacity=0.10, color=C_EL).encode(y=alt.Y("y1:Q", scale=y_scale), y2=alt.Y2("y2:Q"))
# Scatter: individual test specimens
points = (
alt.Chart(df)
.mark_point(size=180, filled=True, opacity=0.75, color=BRAND, stroke=PAGE_BG, strokeWidth=0.8)
.encode(
x=alt.X("cycles:Q", scale=x_scale, title="Cycles to Failure (N)"),
y=alt.Y("stress:Q", scale=y_scale, title="Stress Amplitude (MPa)"),
tooltip=["cycles:Q", "stress:Q"],
)
)
# Basquin power-law fit line
fit_line = (
alt.Chart(fit_df)
.mark_line(strokeWidth=2.5, opacity=0.85, color=BRAND)
.encode(x=alt.X("cycles:Q", scale=x_scale), y=alt.Y("stress:Q", scale=y_scale))
)
# Reference horizontal rules — longer dash pattern to distinguish from grid
ref_rules = (
alt.Chart(ref_df)
.mark_rule(strokeDash=[14, 6], strokeWidth=3)
.encode(
y=alt.Y("stress:Q", scale=y_scale),
color=alt.Color(
"property:N",
scale=alt.Scale(domain=["UTS: 520 MPa", "YS: 380 MPa", "EL: 150 MPa"], range=[C_UTS, C_YS, C_EL]),
legend=alt.Legend(
title="Material Properties", titleFontSize=12, labelFontSize=10, labelLimit=200, orient="bottom-right"
),
),
)
)
# Region text annotations — label the three fatigue life zones
region_labels = (
alt.Chart(region_df)
.mark_text(fontSize=12, fontStyle="italic", align="left", baseline="top", color=INK_SOFT)
.encode(x=alt.X("cycles:Q", scale=x_scale), y=alt.Y("stress:Q", scale=y_scale), text="label:N")
)
# Compose all layers — inner view 620×320 so vl-convert padding fits within 3200×1800
chart = (
(band + points + fit_line + ref_rules + region_labels)
.properties(
width=620,
height=320,
background=PAGE_BG,
padding={"left": 0, "right": 0, "top": 0, "bottom": 0},
title=alt.Title(TITLE, fontSize=16),
)
.configure_view(fill=PAGE_BG, strokeOpacity=0, continuousWidth=620, continuousHeight=320)
.configure_axis(
domainColor=INK_SOFT,
domainOpacity=1,
tickColor=INK_SOFT,
gridColor=INK,
gridOpacity=0.06,
labelColor=INK_SOFT,
titleColor=INK,
labelFontSize=10,
titleFontSize=12,
)
.configure_axisX(gridOpacity=0)
.configure_title(color=INK, fontWeight="bold", fontSize=16)
.configure_legend(
fillColor=ELEVATED_BG,
strokeColor=INK_SOFT,
labelColor=INK_SOFT,
titleColor=INK,
titleFontSize=12,
labelFontSize=10,
)
)
# Save PNG and interactive HTML
chart.save(f"plot-{THEME}.png", scale_factor=4.0)
# PAD-only to exact 3200×1800 — raise if vl-convert overshoots (do NOT crop)
TW, TH = 3200, 1800
_img = Image.open(f"plot-{THEME}.png").convert("RGB")
_w, _h = _img.size
if _w > TW or _h > TH:
raise SystemExit(
f"altair vl-convert produced {_w}×{_h}, exceeds target {TW}×{TH}. "
f"Shrink chart .properties(width=, height=) values and re-render."
)
if _w < TW or _h < TH:
_canvas = Image.new("RGB", (TW, TH), PAGE_BG)
_canvas.paste(_img, ((TW - _w) // 2, (TH - _h) // 2))
_canvas.save(f"plot-{THEME}.png")
chart.save(f"plot-{THEME}.html")
Part of S-N Curve (Wöhler Curve) on anyplot.ai.